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January 8th, 2016, 12:02 PM   #1
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Finding the area of parallelogram? Sides given in linear equations

"Find the area of a parallelogram bounded by the y-axis, the line x =3, the line f(x)=1+2x, and the line parallel to f(x) passing through (2, 7)."

Okay, so a few things I don't understand here. I'm not a native English speaker, so please allow me some leeway. What does it mean for a parallelogram to be bounded by the y-axis?
From the above, one line is vertical (x=3)
second line is f(x)=2x+1, third line and parallel to this would be

7=2(2)+b
b=3 or g(x)=2x+3

So now we have x=3,2x+1 and 2x+3
The area of a paralellogram is height*base.
Height can be found by the distance between any two points on the two parallel lines. For line g(x) we already have 2,7. at x=3 f(x) would return 5
so now we have 2,7 and 2,5
using
d=root((2-2)^2 + (7-5)^2)
we get 2

Now we have height=2.
How do I find the base now? I mean, we are just given two equations of the line; how do I find where the lines begin and where they end? (i.e the domain). Can somebody help me out with this?

Here's the graph
https://www.desmos.com/calculator/n8gv0l2vx8

Last edited by skipjack; January 8th, 2016 at 03:15 PM.
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January 8th, 2016, 12:43 PM   #2
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The side parallel to x=3 is the y axis, which is x=0. Therefore, the base is 3 wide, so the area is 6.
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